Research

• Green's function method in condensed matter physics.

Particles, in quantum mechanics, are represented in quantum wave functions. Meanwhile, physical fields (such as electromagnetic field, gravitational field, etc.) are usually treated classically. This treatment is the "first quantization." The limitation of the first quantization is the difficulty of solving many-particle problems. Then, there is the "second quantization," which treats fields in a quantized fashion as field operators. Along with the statistical mechanics (of multiple states of particles), we can define Green's function to link the field operators with correlation functions and the concept of density of states (DOS).

For example, we can rewrite the Fermi-Dirac distribution function in terms of the summation of Green's function:

• Fully ab initio Eliashberg calculation.

Eliashberg has successfully re-formulated the Bardeen, Cooper, and Schrieffer (BCS) theory of superconductivity with Green's function formalism. The Eliashberg method has allowed systematic corrections in the calculation through the perturbation series. Despite the power of this method, computational costs are an issue to be tackled if one aims to calculate superconductivity without any adjustable parameter (fully ab initio). In particular, the cost of Eliashberg calculation rises with decreasing temperature, while, factually, there are not many high-temperature superconductors yet. 

Our group and collaborators try to mitigate this problem by employing a compact intermediate-representation (IR) of Green's function. The developers named it IR basis functions (SpM-lab/irbasis). Instead of defining on a uniform mesh of imaginary frequencies, this sparse sampling method still results in notable accuracy, given that the method considers enough sampling points in the low-frequency regime.

• High-temperature superconductivity in hydrogen-rich materials.

The first high-temperature superconductors are the cuprates from the lanthanum-based cuprate (35 K, Nobel Prize in Physics 1987), the yttrium-based cuprate (90 K), and the maximum known one (133 K). The conventional explanation does not work on these superconductors, which leaves us with the term "unconventional superconductors". The conventional superconductivity is mediated by atomic vibration in crystals. The lighter the atomic mass, the higher the vibrational frequency, and the bigger the chance that materials superconduct. The first-known superconductor with such a property was MgB2 (39 K), with molar mass of 46 g/mol.

We can technically add megabars pressure to stabilize the stiffness of vibrations. The technique is called chemical precompression. Scientists have already confirmed this kind of superconductivity, even breaking the temperature record, in H3S (200 K) and LaH10 (250 Kelvin). They both are hydrogen-based materials and hydrogen is the lightest element.